🇨🇳【空间·数·守望者】🇨🇳（2022·对合版）🇨🇳

〖若1〗f4(n) = (2*15*20*5)ⁿ+(11*1*16*14)ⁿ+(6*10*19*7)ⁿ+(2*11*12*17)ⁿ+(5*10*9*18)ⁿ+(3*19*4*16)ⁿ+(13*3*15*11)ⁿ+(8*4*10*20)ⁿ+(18*1*6*17)ⁿ+(2*18*8*14)ⁿ+(1*9*19*13)ⁿ+(7*3*20*12)ⁿ+(14*4*9*15)ⁿ+(12*6*16*8)ⁿ+(17*5*13*7)ⁿ = 3000ⁿ+2464ⁿ+7980ⁿ+4488ⁿ+8100ⁿ+3648ⁿ+6435ⁿ+6400ⁿ+1836ⁿ+4032ⁿ+2223ⁿ+5040ⁿ+7560ⁿ+9216ⁿ+7735ⁿ
〖又1〗g4(n) = (19*6*1*16)ⁿ+(10*20*5*7)ⁿ+(15*11*2*14)ⁿ+(19*10*9*4)ⁿ+(16*11*12*3)ⁿ+(18*2*17*5)ⁿ+(8*18*6*10)ⁿ+(13*17*11*1)ⁿ+(3*20*15*4)ⁿ+(19*3*13*7)ⁿ+(20*12*2*8)ⁿ+(14*18*1*9)ⁿ+(7*17*12*6)ⁿ+(9*15*5*13)ⁿ+(4*16*8*14)ⁿ = 1824ⁿ+7000ⁿ+4620ⁿ+6840ⁿ+6336ⁿ+3060ⁿ+8640ⁿ+2431ⁿ+3600ⁿ+5187ⁿ+3840ⁿ+2268ⁿ+8568ⁿ+8775ⁿ+7168ⁿ
【则1】当 n = 0,1,2,3 时，f4(n) = g4(n)
其中，当 n = 0 时，f4(0) = 15 = g4(0)；当 n = 1 时，f4(1) = 80157 = g4(1)；当 n = 2 时，f4(2) = 512070699 = g4(2)；当 n = 3 时，f4(3) = 3637500413745 = g4(3)。

〖若2〗f3(n) = (15*20*5+20*5*2+5*2*15+2*15*20)ⁿ+(1*16*14+16*14*11+14*11*1+11*1*16)ⁿ+(10*19*7+19*7*6+7*6*10+6*10*19)ⁿ+(11*12*17+12*17*2+17*2*11+2*11*12)ⁿ+(10*9*18+9*18*5+18*5*10+5*10*9)ⁿ+(19*4*16+4*16*3+16*3*19+3*19*4)ⁿ+(3*15*11+15*11*13+11*13*3+13*3*15)ⁿ+(4*10*20+10*20*8+20*8*4+8*4*10)ⁿ+(1*6*17+6*17*18+17*18*1+18*1*6)ⁿ+(18*8*14+8*14*2+14*2*18+2*18*8)ⁿ+(9*19*13+19*13*1+13*1*9+1*9*19)ⁿ+(3*20*12+20*12*7+12*7*3+7*3*20)ⁿ+(4*9*15+9*15*14+15*14*4+14*4*9)ⁿ+(6*16*8+16*8*12+8*12*6+12*6*16)ⁿ+(5*13*7+13*7*17+7*17*5+17*5*13)ⁿ = 2450ⁿ+3018ⁿ+3688ⁿ+3290ⁿ+3780ⁿ+2548ⁿ+3654ⁿ+3360ⁿ+2352ⁿ+3032ⁿ+2758ⁿ+3072ⁿ+3774ⁿ+4032ⁿ+3702ⁿ
〖又2〗g3(n) = (6*1*16+1*16*19+16*19*6+19*6*1)ⁿ+(20*5*7+5*7*10+7*10*20+10*20*5)ⁿ+(11*2*14+2*14*15+14*15*11+15*11*2)ⁿ+(10*9*4+9*4*19+4*19*10+19*10*9)ⁿ+(11*12*3+12*3*16+3*16*11+16*11*12)ⁿ+(2*17*5+17*5*18+5*18*2+18*2*17)ⁿ+(18*6*10+6*10*8+10*8*18+8*18*6)ⁿ+(17*11*1+11*1*13+1*13*17+13*17*11)ⁿ+(20*15*4+15*4*3+4*3*20+3*20*15)ⁿ+(3*13*7+13*7*19+7*19*3+19*3*13)ⁿ+(12*2*8+2*8*20+8*20*12+20*12*2)ⁿ+(18*1*9+1*9*14+9*14*18+14*18*1)ⁿ+(17*12*6+12*6*7+6*7*17+7*17*12)ⁿ+(15*5*13+5*13*9+13*9*15+9*15*5)ⁿ+(16*8*14+8*14*4+14*4*16+4*16*8)ⁿ = 2338ⁿ+3450ⁿ+3368ⁿ+3514ⁿ+3612ⁿ+2492ⁿ+3864ⁿ+2982ⁿ+2520ⁿ+3142ⁿ+2912ⁿ+2808ⁿ+3870ⁿ+3990ⁿ+3648ⁿ
【则2】当 n = 0,1,2,3,4 时，f3(n) = g3(n)
其中，当 n = 0 时，f3(0) = 15 = g3(0)；当 n = 1 时，f3(1) = 48510 = g3(1)；当 n = 2 时，f3(2) = 160931868 = g3(2)；当 n = 3 时，f3(3) = 546131955096 = g3(3)；当 n = 4 时，f3(4) =1890192651670896 = g3(4)。